Probability Models of Juridical Proof: It's Time to Kick Bayes Out on His Posterior

Abstract

The application of probability theory to the study of juridical has long been dominated by the Bayesian decision paradigm. I argue that the classical hypothesis-test paradigm is unambiguously better-adapted to the task, for several reasons. The fact-finder's Bayesian prior is poorly defined or undefined and unreliable in close cases; the associated posterior discards information as to the precision of the estimate of the likelihood ratio, to no apparent advantage; and the Bayesian model is vulnerable to well-known proof paradoxes that unnecessarily weaken the effort to model the fact-finding process mathematically. The single strongest argument to prefer Bayes is that the legal system values erroneous trial outcomes for Plaintiff and those for Defendant as equally bad. In this article, I demonstrate that the classical model suffers none of the enumerated weaknesses of the Bayesian model, and that there are many reasons to doubt the Bayesians' postulated loss function. I argue, instead, that the legal system values not trial outcomes but rather litigation outcomes (i.e. from the filing of the lawsuit to the collection of any judgment) evenly. Finally, I propose an alternative approach to modeling the process of juridical proof, based in the theory of linear regression and its attractive properties for efficient prediction of the truth of the elements of Plaintiff's claim.